运筹学与控制论讨论班——A divide-and-conquer approach for the analysis and Bayesian inference of high-dimensional noisy gene expression networks
Title: A divide-and-conquer approach for the analysis and Bayesian inference of high-dimensional noisy gene expression networks
Abstract: Intracellular gene expression systems are inevitably random due to low molecular counts. Consequently, mechanistic models for gene expression should be stochastic, and central to the analysis and inference of such models is solving the Chemical Master Equation (CME), which characterizes the probability evolution of the randomly evolving copy-numbers of the reacting species. While conventional methods such as Monte-Carlo simulations and finite state projections exist for estimating CME solutions, they suffer from the curse of dimensionality, significantly decreasing their efficacy for high-dimensional systems. Here, we propose a new computational method that resolves this issue through a novel divide-and-conquer approach. Our method divides the system into a leader system and several conditionally independent follower subsystems. The solution of the CME is then constructed by combining Monte Carlo estimation for the leader system with stochastic filtering procedures for the follower subsystems. We develop an optimized system decomposition, which ensures the low-dimensionality of the sub-problems, thereby allowing for improved scalability with increasing system dimension. The efficiency and accuracy of the method are demonstrated through several biologically relevant examples in high-dimensional estimation and Bayesian filtering problems. We demonstrate that our method can successfully identify a yeast transcription system at the single-cell resolution, leveraging mRNA time-course microscopy data from real biological experiments, allowing us to rigorously examine the heterogeneity in rate parameters among isogenic cells cultured under identical conditions.
Bio: Dr. Zhou Fang is currently a postdoctoral researcher at ETH Zurich. He received a B.Sc. degree in Computational Mathematics from Zhejiang University in 2014. Later, he received a Ph.D. degree in Operational Research and Cybernetics from Zhejiang University in 2019. His research interest lies in the interface of mathematical control theory, computational sciences, probability, and biology. His primary goal is to develop computational methods and theoretical principles to unravel emergent phenomena in biology and facilitate the control and rational engineering of living cells.